Hyperbolic Mass in 2+1 Dimensions

2025/08/31 by Raphaela Wutte, Wutte, Raphaela
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th) #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.2509.00994

openalex publication_date 2025/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

This short review surveys mass for two-dimensional asymptotically locally hyperbolic initial data sets. I explain the difficulties in defining mass in spatial dimension two, which are resolved via minimisation using a positive energy theorem, and review how gluing theorems can be used to construct novel initial data sets with controlled mass.

Citations

• The Constraint Equations
• The mass of asymptotically hyperbolic Riemannian manifolds

Related

• On Jang's equation and the Positive Mass Theorem for asymptotically hyperbolic initial data sets with dimensions above three and below eight
• A density theorem for asymptotically hyperbolic initial data satisfying the dominant energy condition
• Gluing-at-infinity of two-dimensional asymptotically locally hyperbolic manifolds
• Mass in the Hyperbolic Plane
• Mass and polyhedra in asymptotically hyperbolic manifolds